"There are a couple of apples" or "there is a couple of apples"?

You have only one couple of apples, so it's singular.
There are multiple apples, so it's plural.

Which one is right, "there are a couple of apples" or "there is a couple of apples"? I have seen both used.

In Dutch you would say "there is a couple of apples" because you only have one couple of apples. How about English?

There are 3 things that need mentioning here:

1) Couple as a group of two people in a relationship:

In this case you say:

Where is the couple that requested the wedding?

But you would also say:

They are a lovely couple.

2) Couple as a few:

In this case, you use are, examples:

There are a few apples on the table = There are a couple of apples on the table.

3) As in the 2nd case, but contracted:

When you contract in spoken English, this is the special case where you can contract are to is, like this:

There are a couple of apples on the table. => There's a couple of apples on the table.

Because you cannot contract to there're.

It would actually be extremely unlikely for a speaker to be thinking of this "couple of apples" as a coherent single unit. In OP's context, it simply means two - feasibly three, but probably no more.

Victorian grammarians argued that "a couple" can only be a singular noun. That's pedantic tosh, obviously, but wholesale disregard for this counter-intuitive "rule" has been a long time coming.

The choice depends on how you regard the apples. There are emphasises the fact that there are two separate apples on the table. There is, or more frequently, as Rimmer says, there’s, emphasises the collection, even though it’s a collection of just two (or perhaps two or three, given the imprecise nature of couple).